What options are there for high quality transparent file types?
PNG TGA TIFF openEXR and JPEG 2000 are the image formats that blender can render to that support transparency.

Here they all are in order from best to worst.

PNG


Universal support
4 channels
Only sRGB color space
8 or 16 bits per channel
small file size, with little compression to image quality.


openEXR


Good support among 3D, image editors, compositors, and editor programs.
Multi channeled, can store an unlimited number of channels.
Any color space
up to 32 bits per channel
Large file size, variable amount of compression.


TIFF


Very good support among 3D, image editors, compositors, and editor programs.
Multi channeled, can store an unlimited number of channels.
Many color spaces Grayscale, RGB, CMYK, CIE Lab*, YCbCr
up to 16 bits per channel
Variable file size, variable amount of compression.
Older, openEXR has become the mainstream replacement of TIFF.


TGA


Very good support (because it is old)
4 channels
sRGB
only 8 bits per channel
Large file size, variable amount of compression.
Older, openEXR has become the mainstream replacement of TGA.


JPEG 2000


Very good support
4 channels
sRGB
up to 32 bits per channel
very small file size, however with compression to image quality.